Neuroanatomical work of Golgi and Ramon y Cajal set the stage for the notion that nervous system operations arose from the interplay amongst its parts. While Golgi considered the brain as a continuous system (reticular), Cajal proposed what became known as the neuron doctrine, in which the eleman-tary unit of brain function, the neuron, was an separable entity, but whose operations were dependent on its input from other neurons. These critical ideas grew in the company of emerging theories of brain function that emphasized the need for interaction between parts. In the early 1940s Warren McCulloch and Walter Pitts gave birth to modern neural network theories by proposing brain function to arise from the network action of binary neurons. Their network dynamics, though simple, resulted in remarkably general computational feats. Reinforcing the concept of network action, in his 1949 book Organization of behavior Donald Hebb proposed the modification of neural connections to be a function of their systematic usage and through such laid the basis for one of the most commonly used learning rules in neural nets. However, it is probably fair to say that the McCulloch-Pitts network model finds its place more appropriately in the lineage of artificial neural networks than in the understanding of the dynamics of biological systems. In subsequent developments, McCulloch-Pitts systems formed the basis for the two-layer "perceptrons" of Rosenblatt (1958), the symmetric Hopfield (1982) networks and Grossberg's Adaptive Resonance Theory (ART) (1976), which extended the computational properties to permit object categorization, com-petitie learning and content-addressable memory (i.e. the system correctly yields an entire memory from any subpart of sufficient size). Parallel developments in the 1940s find their roots in the fields of electronic engineering and control system theory and culminate in the field of Cybernetics pioneered by Norbert Wiener. Cybernetics emphasizes regulatory feedback in living and non-living systems and as such connected functional and neural architectures in the field of neuroscience. Here architectures are composed of functionally defined interconnected components giving rise to teleological mechanisms and emphasizing the purpose of a process or behavior. The notions developed in

Cybernetics are closely interwoven with the thinking of other disciplines related to brain function, including radical constructivism in philosophy and autopoiesis (literally "self-creation") in neurobiology advanced by Heinz von Foerster, Humberto Maturana and Francisco Varela among others. In the late 1960s, Cybernetics as a term was increasingly replaced by Self-organization and in the 1970s and 80s by Complex System Theory. One of the reasons is certainly the adoption of these notions by physicists and its consequent developments in pattern formation, nonlinear dynamics and non-equilibrium systems. Hermann Haken pioneered many of these concepts and summarized these in his seminal paper on Synergetics in Reviews of Modern Physics in 1975.

Empirical evaluation of brain networks took somewhat longer to develop. Though the idea of large-scale network operations was at the base of early ideas of nervous system operations (e.g., Bethe's chain theory, Lashley's ideas of mass action, Hebb's cell assemblies), the technology was insufficient to really capture network dynamics in any quantifiable means. As physiological data were moved from paper storage to digital format, analytic methods sensitive to the dependencies of firing arose. Seminal works of Gerstein in 1970 and later with Aertsen in the late 1980's provide the mathematical and theoretical foundation for the ideas of functional and effective connectivity - ideas that now are "household" terms in neuroscience. In the same period, the pioneering work of Gevins and colleagues, published in Science, showed the interplay of cortical sources measured with EEG in humans could be directly related to different stages in cognitive operations. While these works inspired continued development of network analytic methods in electrophysiology, the measure of brain network interactions has been most prolific in functional neuroimag-ing. Starting first with SPECT and PET, and then functional MRI, there was a new opportunity for comprehensive measures from most of the brain in persons performing a wide range of mental functions. Such data quantified distributed action to be brought to bear on network theories of brain operation. Authors in the current volume were among the first to explore network operations revealed in functional neuroimaging (Friston, Horwitz, Mcintosh). The current state of the field has entire research programs geared specifically to methods of measuring brain network dynamics, with parallel advances in the quantification of the anatomical connectivity.

Contemporary brain theories are deeply rooted in the ideas of dynamic systems, self-organization and large scale connectivity. It is posited that brain function arises from the interaction of connected brain areas, in which functional differentiation is performed by the more peripheral areas, whereas the ensuing cognitive integration rests heavily on the large scale network action. The presence of local and global elements involved in brain dynamics poses novel constraints, unknown to the dynamics and pattern formation mechanisms encountered in physical and chemical systems. To uncover the mechanisms of brain function in networks with various local and global architectures is one of the major challenges we are facing these days.

Our Handbook arose from the fourth in a series of annual meetings focused on brain connectivity ( These intense workshops brought together anatomists, physiologists, cognitive and, computational neuroscientists to discuss the current issues on how to integrate brain connectivity across structural and functional domains. Motivated by the discussions at this and the prior meetings, here we wish to provide an account of the current knowledge on the imaging, analysis and theory of the anatomical and functional connectivity of the brain.

The Handbook on Brain Connectivity would not have been possible without the outstanding contributions of the Handbook authors. All contributors are leading experts in various fields concerning structural and functional brain connectivity. In the first part of the Handbook, the chapters focus upon an introduction and discussion of the principles underlying connected systems in the brain. The second part introduces the currently available non-invasive technologies for measuring structural and functional connectivity in the brain. Part three provides an overview of the analysis techniques currently available and highlights new developments. Part four introduces the application and transfer of the concepts of brain connectivity to behavior, cognition and the clinical domain. We also wish to thank Arpan Banerjee, Ajay Pillai, Murad Qubbaj, Young-Ah Rho, Roxana Stefanescu and Maria Tassopoulos for their tireless editorial help. We are most grateful to Technical Editor Thomas Ditzinger at Springer Pulisher, who has been always available for guidance and advice during the creation of the Handbook.

Viktor K Jirsa Anthony R McIntosh

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